CS244a: An Introduction to Computer Networks

Transcription

1 Do not write in this box MCQ 9: /10 10: /10 11: /20 12: /20 13: /20 14: /20 Total: Name: Student ID #: CS244a Winter 2003 Professor McKeown Campus/SITN-Local/SITN-Remote? CS244a: An Introduction to Computer Networks Final Exam: Thursday March 20, 2003 You are allowed 3 hours to complete this exam. (i) This exam is closed book and closed notes. However, you may refer to a sheet of 8.5"x11" paper (double-sided) of your own design. (ii) Write your solution directly onto this exam. Be sure to write your name and student ID clearly on the front of the exam. (iii) Don t panic! Be sure to start by reading the exam all the way through. Then answer the questions in whatever order you choose. (iv) Show your reasoning clearly. If your reasoning is correct, but your final answer is wrong, you will receive most of the credit. If you just show the answer without reasoning, and your answer is wrong, you may receive no points at all. The Stanford Honor Code In accordance with both the letter and spirit of the Honor Code, I didn't cheat on this exam. Signature: Page 1 of 14

2 Multiple Choice Questions. Instructions: in the following questions, check all listed assertions that appear to be correct. There is at least one correct assertion per question, but there may be more. Each correct assertion checked will earn you one point. For each incorrect assertion you check, you will lose one point. If you don t know an answer, checking no assertion will neither earn you nor lose you any points. 1. Multicast routing. In reverse path broadcast, which of the following are true: (a.) Packets reach every router in the network. (b.) Packets follow the shortest path tree from source to destinations. (c.) Unless a packet arrives to the router on the interface that is on the shortest path to the source, the packet is dropped. (d.) Every router receives exactly one copy of each packet. 2. CSMA/CD. In a CSMA/CD network we require TRANSP > 2PROP because: (a.) TRANSP is the round-trip time from a source to the destination and back again. Therefore, it must be at least twice the one way propagation delay, PROP. (b.) Otherwise, the signal would degrade too much along the wire making it difficult to detect collisions. (c.) The sender needs to unambiguously determine that a packet encountered a collision before it finishes transmitting the packet. (d.) In any network (regardless of whether we use CSMA/CD or not) the transmission time of a packet is a function of both the data rate, and speed of propagation along the wire. 3. Ethernet. In an Ethernet network, which of the following are true: (a.) Ethernet switches (a.k.a bridges) learn addresses by looking at the destination address of packets as they pass by. (b.) Ethernet hubs and repeaters learn addresses by looking at the addresses of packets as they pass by. (c.) A correctly operating Ethernet switch never sends a packet to the wrong outgoing port. (d.) Ethernet switches (a.k.a bridges) learn addresses by looking at the source address of packets as they pass by. (e.) Collisions occur less on a switched Ethernet network because links run faster. 4. Spanning tree protocol for Ethernet switches. A network of Ethernet switches uses the Spanning Tree Protocol so that: (a.) The switch can learn, and build an accurate table of IP addresses. (b.) Packets don t cycle in the network forever. (c.) The port of every switch forwards all the packets it receives. (d.) Packets will follow the shortest path to a destination. Page 2 of 14

3 5. Reliable Flooding. Which of the following are true statements about reliable flooding: (a.) It is used in Distance Vector table exchange protocols enabling neighboring routers to periodically exchange their tables. (b.) It is used in Link State table exchange protocols enabling routers to distribute the state of their links. (c.) Can be achieved only if routers always send packets back through the interface through which they entered the router. (d.) Can be achieved, in part, if packets contain a sequence number and "time to live" field to prevent packets from looping endlessly in the network. (e.) Is an efficient centralized algorithm for calculating routing tables. 6. TCP. Which of the following are true statements about TCP: (a.) The Slow-Start algorithm increases a source s rate of transmission faster than "additive increase". (b.) A source s retransmission timeout value (RTO) is always set equal to the measured RTT. (c.) If RTO is too small, it might lead to unnecessary retranmissions. (d.) A source s retranmission timeout value is set to a value that increases with the variance in measured RTT values. 7. TCP: Which of the following are true statements about TCP: (a.) TCP segments can only be lost when router queues overflow. (b.) If the window size of a TCP connection (measured in seconds) is smaller than the RTT, the link will operate very efficiently. (c.) There is no performance benefit to having a window size (measured in seconds) larger than the RTT. (d.) A receiver reduces the advertized window size in response to congestion at routers along the path. 8.Random Early Detection (RED). Which of the following are true? (a.) RED is tolerant of bursts because it never drops consecutive packets from the same flow. (b.) RED always drops packets, with probability 1, when the router s queue length is greater than the maximum threshold value. (c.) RED attempts to "desynchronize" competing TCP sources by causing them to lose packets at different times. (d.) If two flows, one TCP and one UDP, share a "RED" router, the RED algorithm will ensure that both flows receive an identical share of the outgoing link. Page 3 of 14

4 9. (10 points) Digital Library. We hire you as a consultant to help us design a digital library in which books are scanned, stored digitally and made available to users of the World Wide Web. The library will Books Channel, B=100MHz Disc Storage The Internet Users contain ten million books; we will assume that each book contains 400 white pages containing black text. The text on each page covers 6"x6" and we will represent the text area using 300 dots per inch (dpi) vertically and horizontally. We will represent 1 "dot" with 1 bit and will not use any data compression techniques. We assume that 1,000 users access the library simultaneously and that they request a new page once per minute. The bandwidth of the channel connecting the library to the outside world is 100MHz, and has a capacity that is limited by Gaussian noise. (a.) How many bytes of data storage are required on the disk? (b.) What data rate is required to connect the library to the Internet? (c.) What is the minimum signal to noise ratio that could possibly be tolerated on the channel? Express the signal to noise ratio as both a ratio and in db. Page 4 of 14

5 (d.) We analyze the link, and find that it has a bit error rate (BER) of required to ensure that the packet error rate (PER) is less than you make What packet size is? State any assumptions 10. (10 points) Queues. Every second, a train of 100 bits arrive to a queue at rate 1000 bits/second. The departure rate from the queue is 500 bits/second. (a.) What is the average queue occupancy? (b.) What is the average delay of a bit in the queue? Page 5 of 14

6 (c.) If the trains of 100 bits arrived at random intervals, one train per second on average, would the average queue occupancy be the same, lower or higher than in part (a)? Justify your answer. (d.) If the departing bits from the queue are fed into a second, identical queue with the same departure rate, what is the average occupancy of the second queue? Page 6 of 14

7 11. (20 points) Multicast Routing. Consider the network topology shown below. It is the same topology you saw on the midterm. The topology consists of multiple routers interconnected by links. Each link has a static cost associated with it which represents the cost of sending data over that link. For example, the link from F to D has a cost of 3. Most of the links are symmetric (i.e. the cost is the same in both directions, such as between D and F), whereas one is asymmetric (i.e. the cost is different in each direction between F and E). 14 H 2 G 4 B F 3 D 2 A 8 1 E C 4 (a.) Using an algorithm we saw in class (you choose which one), find the shortest path multicast tree for packets from source router D to every other router in the network. In other words, find the tree in which every packet follows the shortest path from D to its destination. Carefully explain each step of your algorithm. Sketch the resulting multicast tree. Page 7 of 14

8 (b.) We could define the multicast tree another way. We ll call the tree the lowest total cost tree if it minimizes the sum of the costs in the tree, and connects D to every other router. In general (in other words, for networks in general, not just this example), will the lowest total cost tree the same as the type of tree we found in part (a)? Explain your answer. 12. (20 points) TCP Congestion Control. In this question we ll find approximate equations for the throughput of the TCP AIMD mechanism. This question is the same as the one on the midterm; and is a question most students avoided! Keep your wits about you - the questions is not as hard as it looks. (a.) Why does TCP use additive increase rather than multiplicative increase? Page 8 of 14

9 The graph below shows the "sawtooth" evolution of the TCP sender s window size as a function of time. W is the maximum window size (measured in packets). In this question, assume that all packets are P bits long, and that exactly one packet is dropped every time the window size reaches W. window size W time (b.) If we ignore the "slow-start" phase at the beginning of the flow, show that the average rate at which the transmitter sends packets is given by: R = 3 W packets per second. 4 RTT RTT is the round-trip time, which we will assume is constant. (c.) Show that the fraction of packets dropped, L, is given by the following expression: L = W --W Hint: Remember that we re assuming that exactly one packet is dropped every time the window size reaches W. Page 9 of 14

10 (d.) Using your answers to (b) and (c), and assuming that W is very large, show that the average rate at which the transmitter sends is given by: P R P bits per second. L RTT L RTT Page 10 of 14

11 (e.) The goodput of a TCP connection is defined to be the rate at which data is sent once. i.e. the rate does not include data that is retransmitted. Is the goodput rate smaller or larger than R? (f.) Assuming that one window s worth of data is retransmitted every time a packet is dropped, rewrite the equation in (d) to show the goodput of the flow. 13. (20 points) Weighted Fair Queueing. The figure below shows n leaky-bucket flows multiplexed together onto a link at rate C bytes per second. The i-th leaky-bucket contains at most k i tokens; and new tokens arrive at rate r i tokens per second. One token is required for each byte transmitted into the network. Each flow has its own FCFS queue. Flow i is served with weight w i by a WFQ scheduler. r 1 k1 leaky-bucket regulator r n kn w 1 w n WFQ C leaky-bucket regulator (a.) Assuming that the WFQ scheduler serves one byte at a time, prove that no queue will overflow if, and only if, (for all i): r i < C( w i w j ) n j = 1 Page 11 of 14

12 (b.) Assuming that no queue overflows, show that the maximum queueing delay encountered by a byte is given by: dˆ i = k i n C( w i w j ) j = 1 (c.) If we placed another leaky bucket in front of each of the leaky-buckets above, with the same parameters (i.e. r i and k i are the same for both leaky-buckets), would bytes ever have to wait at the second leaky-bucket? Justify your answer. Page 12 of 14

13 (d.) Now imagine that we want to control the peak rate of each flow, p i as well as its average rate. Show how a second leaky-bucket placed in series with the first can do this. Be sure to give the bucket size and token generation rate for the second leaky-bucket. 14. (20 points) Token passing. Consider the token passing ring network shown below. Each time a host grabs the token, it can send one packet. In this network, the token does not pass from each host around the ring in turn; instead, as soon as a host has finished transmitting a packet, it picks another host uniformly and at random from the set of hosts (excluding itself), and sends it the token. The token has a destination address, just like a normal packet. When a host receives the token, it can hold onto it while it transmits a packet, or if it has no packets to send, it forwards it immediately to another host picked at random. Packets and tokens can only be sent clockwise around the ring. Assume that all packets take TRANSP seconds to transmit, that the token is small compared to a packet, that the propagation time of a bit around the ring is PROP, and that the N hosts are equally spaced around the ring.. H N H 1 H 2 (a.) Derive an expression for the efficiency of the network. Assume that a host transmits one packet every time it receives the token Page 13 of 14

14 (b.) Now assume that when a host passes the token, it might "pass" it to itself. If it does so, it doesn t send the token around the ring. It just holds onto it and sends another packet. Rewrite the expression for efficiency in this case. (c.) Consider now the bus network shown below. It is essentially the same as the ring network above, but host N is not connected to host 1. The hosts are equally spaced along the bus, and the propagation delay along the bus is PROP. When transmitted, packets flow in both directions along the bus and do not reflect from the ends. The token is passed from one host to another in the same random way as in part (b). In other words, a host picks another host (including itself) uniformly and at random from among all N hosts. Is the efficiency of this network higher, or lower than for the ring network above? You don t have to derive an expression for the efficiency (you can if you d like, but it s not necessary), but you do need to justify your answer. H 1 H 2 H N Page 14 of 14